Pencil-beam approximation of fractional Fokker-Planck

TL;DR

This paper models light beam propagation in turbulent media using fractional Fokker-Planck equations and demonstrates that fractional Fermi pencil-beam models accurately approximate beam spreading in the small diffusion limit, with quantifiable error bounds.

Contribution

It introduces a fractional Fermi pencil-beam approximation for highly forward-peaked turbulent media and provides an error estimate in the 1-Wasserstein distance.

Findings

Beam spreading is accurately captured by the fractional Fermi pencil-beam model.

The approximation error is quantified in the small diffusion limit.

The model effectively describes light propagation in turbulent media.

Abstract

We consider the modeling of light beams propagating in highly forward-peaked turbulent media by fractional Fokker-Planck equations and their approximations by fractional Fermi pencil-beam models. We obtain an error estimate in a 1-Wasserstein distance for the latter model showing that beam spreading is well captured by the Fermi pencil-beam approximation in the small diffusion limit.